Question

A man of height 1.7 meters walks away from a 5- meter lamppost at a speed of 1.1 m/s. Find the rate at which his shadow is increasing in length.

An illustration shows a man walking past a lamp post. The lamp is 5 units above the ground. The man is horizontally x units away from lamp. A line is drawn from the lamp to the man’s head and is extended to the ground. The distance between the man and the point on the ground where the line ends is labeled y.

(Use decimal notation. Give your answer to three decimal places.)

Answer 1

when the man is x meters from the pole, if the shadow's length is s, then
(s+x)/5 = s/1.7
s = 1.7/3.5 x
so, with dx/dt = 1.1,
ds/dt = 1.7/3.5 * dx/dt = 0.534 m/s